Zero-sum tiling game

Abstract

A zero-sum tiling game. A plurality of “domino-like” game pieces include indicia viewable on the top surfaces of the game pieces that correspond to one, or the other, or both of two halves of the game pieces. The indicia forms a binary set. The indicia associated with one half of the game piece may be summed to indicate the value for that type of indicia for that one half of the game piece, while the indicia may more generally be “added” or “summed” overall to obtain an overall value for any desired number of halves. Particularly, it is an object of the game to lay down game pieces in such a way that each piece that is laid down completes a square that consists of four halves, wherein the sum of the indicia for the four halves is zero.

1. A zero-sum tiling game, comprising a set of domino-like game pieces having two halves, said set comprising at least six game pieces and indicia associated therewith that may be just one of two types, wherein the indicia for at least one of said game pieces includes both said types, wherein the indicia for at least two of said game pieces includes just one of said types, wherein the indicia for at least two of said game pieces includes just the other of said types, wherein said two types of indicia associated with the game pieces are of opposite polarity, and wherein at least one of said game pieces has no indicia associated therewith. 
   
   
     2. The zero-sum tiling game of  claim 1 , wherein there are at least twenty-eight of said game pieces, wherein the indicia for at least nine of said game pieces includes both said types, wherein the indicia for at least nine of said game pieces includes just one of said types, wherein the indicia for at least nine of said game pieces includes just the other of said types. 
   
   
     3. A method for constructing a zero-sum tiling game, comprising:
 providing for the laying down of a first domino-like game piece having a first integer number of indicia of one of two opposite polarity types, wherein said first number is greater than or equal to zero, and a second integer number of indicia of the other of said polarity types, wherein said second number is greater than or equal to zero; and 
 defining a subsequent move wherein a player subsequently lays down a subsequent domino-like game piece aligned with and adjacent said first game piece, said subsequent game piece having a third integer number of indicia of said one of said two polarity types, wherein said third number is greater than or equal to zero, and a fourth integer number of indicia of said other of said two polarity types, wherein said fourth number is greater than or equal to zero; 
 wherein it is predefined that said subsequent move is legal when the sum of said first and third numbers equals the sum of said second and fourth numbers, and wherein, otherwise, said move is not legal. 
 
   
   
     4. A method for constructing a zero-sum tiling game, comprising:
 providing for the laying down of a first domino-like game piece having two halves, wherein one of the halves includes a first integer number of indicia of one of two opposite polarity types, wherein said first number is greater than or equal to zero, and a second integer number of indicia of the other of said polarity types, wherein said second number is greater than or equal to zero; 
 providing for the laying down of a second domino-like game piece having two halves, wherein one of the halves of said second game piece is adjacent said one of the halves of said first game piece, wherein said one of the halves of said second game piece includes a third integer number of indicia of said one of said polarity types, wherein said third number is greater than or equal to zero, and a fourth integer number of indicia of said other of said polarity types, wherein said fourth number is greater than or equal to zero; and 
 defining a subsequent move wherein a player subsequently lays down a subsequent domino-like game piece having two halves, wherein one of the halves of said subsequent game piece is adjacent said one half of said first game piece and the other half of said subsequent game piece is adjacent said one half of said second game piece, said subsequent game piece having a fifth integer number of indicia of said one of said polarity types, wherein said fifth number is greater than or equal to zero, and a sixth integer number of indicia of the other of said polarity types, wherein said sixth number is greater than or equal to zero; 
 wherein it is predefined that said subsequent move is legal when the sum of said first, third and fifth numbers is equal to the sum of said second, fourth and sixth numbers, and wherein, otherwise, said move is not legal. 
 
   
   
     5. The method of  claim 4 , wherein at least one of said first and second numbers is equal to zero, and at least one of said third and fourth numbers is equal to zero. 
   
   
     6. The method of  claim 5 , wherein said halves are squares and wherein two of said squares are adjacent one another when they form a rectangle. 
   
   
     7. A method for constructing a zero-sum tiling game, comprising:
 providing for the laying down of a first domino-like game piece having two halves, wherein one of the halves includes a first integer number of indicia of one of two opposite polarity types, wherein said first number is greater than or equal to zero, and a second integer number of indicia of the other of said polarity types, wherein said second number is greater than or equal to zero; 
 providing for the laying down of a second domino-like game piece having two halves, wherein one of the halves of said second piece is adjacent said one of the halves of said first game piece, wherein said one of the halves of said second game piece includes a third integer number of indicia of said one of said polarity types, wherein said third integer is greater than or equal to zero, and a fourth integer number of indicia of the other of said polarity types, wherein said fourth, number is greater than or equal to zero; 
 providing for the laying down of a third domino-like game piece having two halves, wherein one of the halves of said third game piece is adjacent said one of the halves of said second game piece, wherein said one of the halves of said third game piece includes a fifth integer number of indicia of said one of said polarity types, wherein said fifth integer is greater than or equal to zero, and a sixth integer number of indicia of the other of said polarity types, wherein said sixth integer is greater than or equal to zero; 
 defining a subsequent move wherein a player subsequently lays down a subsequent domino-like game piece having two halves, wherein one of the halves of said subsequent game piece is adjacent said one of the halves of said third game piece, wherein said one of the halves of said subsequent game piece includes a seventh integer number of indicia of said one of said polarity types, wherein said seventh number is greater than or equal to zero, and an eighth integer number of indicia of the other of said polarity types, wherein said eighth number is greater than or equal to zero; 
 wherein it is predefined that said subsequent move is legal when the sum of said first, third, fifth, and seventh numbers is equal to the sum of said second, fourth, sixth and eighth numbers, and wherein, otherwise, said move is not legal. 
 
   
   
     8. The method of  claim 7 , wherein at least one of said first and second numbers is equal to zero, at least one of said third and fourth numbers is equal to zero, at least one of said fifth and sixth numbers is equal to zero, and at least one of said seventh and eighth numbers is equal to zero. 
   
   
     9. The method of  claim 8 , wherein said halves are squares and wherein two of said squares are adjacent one another when they form a rectangle. 
   
   
     10. A zero-sum tiling game, comprising:
 a first plurality of game pieces of substantially identical shape and size, wherein first game indicia are distributed over said first plurality of game pieces so that each game piece has a unique combination of first and second integer numbers of said first game indicia, said first integer number ranging inclusively between zero and a predetermined maximum number of the first game indicia, and said second integer number ranging inclusively between a value of the first integer number and the predetermined maximum number; 
 a second plurality of game pieces of substantially identical shape and size as said first plurality of game pieces, wherein second game indicia differing from said first game indicia are distributed over said second plurality of game pieces so that each game piece has a unique combination of third and fourth integer numbers of said second game indicia, said third integer number ranging inclusively between zero and said predetermined maximum number of the second indicia, and said fourth integer number ranging inclusively between a value of the third integer number and the predetermined maximum number, except that one combination 0, 0 for the second indicia is omitted; 
 wherein said first and second indicia are of opposite polarity. 
 
   
   
     11. The zero-sum tiling game of  claim 10 , wherein said predetermined maximum number is equal to three, so that there are 10 of said unique combinations, including one combination corresponding to both said first and second integers being equal to zero. 
   
   
     12. The zero-sum tiling game of  claim 10 , comprising a plurality of third game pieces of substantially identical shape and size as said first and second pluralities of game pieces, said third plurality of game pieces having a unique combination of a fifth integer number of the first indicia ranging between one and the predetermined maximum number, and a sixth integer number of the second indicia ranging between one and the predetermined number.